Question: Find the product of all integer divisors of $105$ that also divide $14$.  (Recall that the divisors of an integer may be positive or negative.)
Explanation: The factors of $105$ are $\pm 1, \pm 3, \pm 5, \pm 7, \pm 15, \pm 21, \pm 35, \pm 105$.  Of these, only $\pm 1$ and $\pm 7$ divide $14$.  Their product is $-7\cdot -1\cdot 1\cdot 7 = \boxed{49}$.